Subjects

Maths

Geometry and measure

Angles, lines and polygons

GCSE Higher Maths Notes 2019-2024 | Formulas, Geometry, Pythagoras & Trigonometry

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GCSE Higher Maths Notes 2019-2024 | Formulas, Geometry, Pythagoras & Trigonometry

Olamide

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A comprehensive guide to GCSE Higher Mathematics geometry, focusing on essential formulas, theorems, and mathematical concepts. This guide covers everything from basic angle facts to complex geometric principles and number operations.

• The document is structured into key sections including geometry fundamentals, circle theorems, trigonometry, and algebraic concepts
• Includes detailed coverage of Pythagoras and trigonometry study guide materials with essential formulas and applications
• Features comprehensive surface area and volume formulas for GCSE math calculations
• Contains important angle facts, polygon properties, and transformation descriptions
• Incorporates number operations including FDP (Fractions, Decimals, Percentages) and standard form

...

27/07/2023

5256

GEOMETRY
A) Angle facts - lines
1 Vertically opposite angles
2
3
4
5
6
15
16
17
18
D) Congruence and similarity
The four tests for
congruenc

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Page 2: Advanced Geometry and Circle Theorems

This page delves into more advanced geometry topics and circle theorems, essential for the GCSE Maths topics list Edexcel Higher Paper 1.

Circles

The section on circles covers key formulas and concepts:

Circumference = π × diameter
Area = πr²
Area of a sector formula
Arc length formula

Highlight: Remember the mnemonic "Circumference is pi times diameter, pi times diameter, pi times diameter" to recall the circumference formula easily.

Pythagoras and Trigonometry

This part introduces Pythagoras and trigonometry study guide gcse concepts:

Pythagoras' Theorem: a² + b² = c² (where c is the hypotenuse)
Trigonometric ratios: sine, cosine, and tangent (SOHCAHTOA)
Sine and cosine rules
Area of a triangle using trigonometry

Definition: SOHCAHTOA is a mnemonic for remembering trigonometric ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

Describing Transformations

The guide covers four types of transformations:

Rotation: specifying direction, degrees, and center of rotation
Reflection: identifying the line of reflection
Translation: using vector notation
Enlargement: specifying scale factor and center of enlargement

Circle Theorems

This section outlines important circle theorems:

The angle in a semi-circle is 90°
Angles at the circumference in the same segment are equal
Opposite angles in a cyclic quadrilateral add up to 180°
The angle between a tangent and a radius is 90°
The angle at the center is twice the angle at the circumference
Two tangents from the same point are equal in length
Alternate Segment Theorem

Example: In a cyclic quadrilateral ABCD, if angle A = 70° and angle C = 80°, then angle B + angle D must equal 180° - (70° + 80°) = 30°.

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Page 3: Number and Algebra Concepts

This page focuses on number and algebra concepts, crucial for the Edexcel maths specification GCSE Checklist.

FDP (Fractions, Decimals, Percentages)

The section covers conversions and calculations involving fractions, decimals, and percentages:

Percentage increase and decrease
Compound interest and depreciation
Converting fractions to decimals and percentages
Calculating percentage change

Tip: To convert a decimal to a percentage, multiply by 100.

Conversions

This part provides conversion factors for various units:

Length: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m
Area: 1 cm² = 0.0001 m²
Volume: 1 cm³ = 0.000001 m³
Mass: 1 kg = 1000 g
Capacity: 1 l = 1000 ml

Standard Form

The guide explains how to write numbers in standard form:

A number between 1 and 10 multiplied by a power of 10

Example: 40,000 in standard form is 4 × 10⁴

Surds and Indices

This section covers operations with surds and rules for indices:

Simplifying surds
Rationalizing denominators
Index laws for multiplication, division, and powers

Special Numbers

The guide defines special types of numbers:

Factors: numbers that divide into another number without a remainder
Prime numbers: numbers with only two factors (1 and itself)
Multiples: numbers in a given number's times table
Square numbers: numbers multiplied by themselves

Equations and Inequalities

This part introduces solving equations and inequalities:

Like terms in algebra
Inequality symbols and their meanings

Vocabulary: Like terms in algebra have the same variables raised to the same powers.

Equations of Lines, Curves, and Circles

The section concludes with formulas for:

Straight line equations (y = mx + c)
Finding midpoints
Parallel and perpendicular lines
Turning points of curves
Equation of a circle

Definition: In y = mx + c, m represents the gradient (slope) of the line, and c is the y-intercept.

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Page 4: [Note: No content provided for page 4 in the transcript]

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Page 1: Geometry Fundamentals

This page covers fundamental geometry concepts essential for GCSE higher math geometry notes 2019 2020 pdf.

Angle Facts - Lines

The section begins with angle facts related to lines, including:

Vertically opposite angles are equal
Angles on a straight line add up to 180°
Angles at a point add up to 360°
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°

Definition: Vertically opposite angles are angles opposite each other when two lines intersect.

Angle Facts - Triangles and Quadrilaterals

This section covers angle properties in triangles and quadrilaterals:

Angles in a triangle add up to 180°
Base angles of an isosceles triangle are equal
Angles in an equilateral triangle are all 60°
Angles in a quadrilateral add up to 360°

Highlight: Understanding these angle properties is crucial for solving complex geometry problems in GCSE maths.

Angle Facts - Polygons

The guide provides information on polygon angles:

Exterior angles of a polygon add up to 360°
The interior and exterior angle of any polygon add up to 180°
The sum of interior angles formula: (number of sides - 2) × 180°
Regular polygons have all sides and angles equal

Congruence and Similarity

This section outlines the four tests for congruence (SSS, ASA, SAS, RHS) and conditions for similar triangles.

Vocabulary: Congruence means two shapes are identical in size and shape.

Area Formulas

The page concludes with area formulas for various shapes:

Rectangle: length × width
Parallelogram: base × perpendicular height
Triangle: ½ × base × perpendicular height
Trapezium: ½(a + b) × h

Example: The area of a trapezium can be remembered with the rhyme: "Half the sum of the parallel sides, times the distance between them. That is how you calculate the area of a trapezium."

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Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

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Knowunity is the #1 education app in five European countries

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iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

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Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Subjects

Maths

Geometry and measure

Angles, lines and polygons

GCSE Higher Maths Notes 2019-2024 | Formulas, Geometry, Pythagoras & Trigonometry

...

27/07/2023

5256

10/11

Maths

402

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Page 2: Advanced Geometry and Circle Theorems

This page delves into more advanced geometry topics and circle theorems, essential for the GCSE Maths topics list Edexcel Higher Paper 1.

Circles

The section on circles covers key formulas and concepts:

Circumference = π × diameter
Area = πr²
Area of a sector formula
Arc length formula

Highlight: Remember the mnemonic "Circumference is pi times diameter, pi times diameter, pi times diameter" to recall the circumference formula easily.

Pythagoras and Trigonometry

This part introduces Pythagoras and trigonometry study guide gcse concepts:

Pythagoras' Theorem: a² + b² = c² (where c is the hypotenuse)
Trigonometric ratios: sine, cosine, and tangent (SOHCAHTOA)
Sine and cosine rules
Area of a triangle using trigonometry

Definition: SOHCAHTOA is a mnemonic for remembering trigonometric ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

Describing Transformations

The guide covers four types of transformations:

Rotation: specifying direction, degrees, and center of rotation
Reflection: identifying the line of reflection
Translation: using vector notation
Enlargement: specifying scale factor and center of enlargement

Circle Theorems

This section outlines important circle theorems:

The angle in a semi-circle is 90°
Angles at the circumference in the same segment are equal
Opposite angles in a cyclic quadrilateral add up to 180°
The angle between a tangent and a radius is 90°
The angle at the center is twice the angle at the circumference
Two tangents from the same point are equal in length
Alternate Segment Theorem

Example: In a cyclic quadrilateral ABCD, if angle A = 70° and angle C = 80°, then angle B + angle D must equal 180° - (70° + 80°) = 30°.

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Improve your grades

Join milions of students

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Page 3: Number and Algebra Concepts

This page focuses on number and algebra concepts, crucial for the Edexcel maths specification GCSE Checklist.

FDP (Fractions, Decimals, Percentages)

The section covers conversions and calculations involving fractions, decimals, and percentages:

Percentage increase and decrease
Compound interest and depreciation
Converting fractions to decimals and percentages
Calculating percentage change

Tip: To convert a decimal to a percentage, multiply by 100.

Conversions

This part provides conversion factors for various units:

Length: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m
Area: 1 cm² = 0.0001 m²
Volume: 1 cm³ = 0.000001 m³
Mass: 1 kg = 1000 g
Capacity: 1 l = 1000 ml

Standard Form

The guide explains how to write numbers in standard form:

A number between 1 and 10 multiplied by a power of 10

Example: 40,000 in standard form is 4 × 10⁴

Surds and Indices

This section covers operations with surds and rules for indices:

Simplifying surds
Rationalizing denominators
Index laws for multiplication, division, and powers

Special Numbers

The guide defines special types of numbers:

Factors: numbers that divide into another number without a remainder
Prime numbers: numbers with only two factors (1 and itself)
Multiples: numbers in a given number's times table
Square numbers: numbers multiplied by themselves

Equations and Inequalities

This part introduces solving equations and inequalities:

Like terms in algebra
Inequality symbols and their meanings

Vocabulary: Like terms in algebra have the same variables raised to the same powers.

Equations of Lines, Curves, and Circles

The section concludes with formulas for:

Straight line equations (y = mx + c)
Finding midpoints
Parallel and perpendicular lines
Turning points of curves
Equation of a circle

Definition: In y = mx + c, m represents the gradient (slope) of the line, and c is the y-intercept.

Sign up to see the content. It's free!

Access to all documents

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Page 4: [Note: No content provided for page 4 in the transcript]

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Access to all documents

Improve your grades

Join milions of students

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Page 1: Geometry Fundamentals

This page covers fundamental geometry concepts essential for GCSE higher math geometry notes 2019 2020 pdf.

Angle Facts - Lines

The section begins with angle facts related to lines, including:

Vertically opposite angles are equal
Angles on a straight line add up to 180°
Angles at a point add up to 360°
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°

Definition: Vertically opposite angles are angles opposite each other when two lines intersect.

Angle Facts - Triangles and Quadrilaterals

This section covers angle properties in triangles and quadrilaterals:

Angles in a triangle add up to 180°
Base angles of an isosceles triangle are equal
Angles in an equilateral triangle are all 60°
Angles in a quadrilateral add up to 360°

Highlight: Understanding these angle properties is crucial for solving complex geometry problems in GCSE maths.

Angle Facts - Polygons

The guide provides information on polygon angles:

Exterior angles of a polygon add up to 360°
The interior and exterior angle of any polygon add up to 180°
The sum of interior angles formula: (number of sides - 2) × 180°
Regular polygons have all sides and angles equal

Congruence and Similarity

This section outlines the four tests for congruence (SSS, ASA, SAS, RHS) and conditions for similar triangles.

Vocabulary: Congruence means two shapes are identical in size and shape.

Area Formulas

The page concludes with area formulas for various shapes:

Rectangle: length × width
Parallelogram: base × perpendicular height
Triangle: ½ × base × perpendicular height
Trapezium: ½(a + b) × h

Example: The area of a trapezium can be remembered with the rhyme: "Half the sum of the parallel sides, times the distance between them. That is how you calculate the area of a trapezium."

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average app rating

17 M

Pupils love Knowunity

#1

In education app charts in 17 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

GCSE Higher Maths Notes 2019-2024 | Formulas, Geometry, Pythagoras & Trigonometry

Page 2: Advanced Geometry and Circle Theorems

Circles

Pythagoras and Trigonometry

Describing Transformations

Circle Theorems

Page 3: Number and Algebra Concepts

FDP (Fractions, Decimals, Percentages)

Conversions

Standard Form

Surds and Indices

Special Numbers

Equations and Inequalities

Equations of Lines, Curves, and Circles

Page 4: [Note: No content provided for page 4 in the transcript]

Page 1: Geometry Fundamentals

Angle Facts - Lines

Angle Facts - Triangles and Quadrilaterals

Angle Facts - Polygons

Congruence and Similarity

Area Formulas

Similar content

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

17 M

#1

950 K+

Still not convinced? See what other students are saying...

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

The app is very simple and well designed. So far I have always found everything I was looking for :D

I love this app ❤️ I actually use it every time I study.

GCSE Higher Maths Notes 2019-2024 | Formulas, Geometry, Pythagoras & Trigonometry

Sign up to see the content. It's free!

Page 2: Advanced Geometry and Circle Theorems

Circles

Pythagoras and Trigonometry

Describing Transformations

Circle Theorems

Sign up to see the content. It's free!

Page 3: Number and Algebra Concepts

FDP (Fractions, Decimals, Percentages)

Conversions

Standard Form

Surds and Indices

Special Numbers

Equations and Inequalities

Equations of Lines, Curves, and Circles

Sign up to see the content. It's free!

Page 4: [Note: No content provided for page 4 in the transcript]

Sign up to see the content. It's free!

Page 1: Geometry Fundamentals

Angle Facts - Lines

Angle Facts - Triangles and Quadrilaterals

Angle Facts - Polygons

Congruence and Similarity

Area Formulas

Similar content

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

17 M

#1

950 K+

Still not convinced? See what other students are saying...

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

The app is very simple and well designed. So far I have always found everything I was looking for :D

I love this app ❤️ I actually use it every time I study.